Question

Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (2,-2)

Answer 1

$\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ y=a(x-{{ h}})^2+{{ k}}\qquad \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0 \\\\\\ y=ax^2\qquad \begin{cases} x=2\\ y=-2 \end{cases}\implies -2=a2^2$

solve for "a", to get the coefficient, and then plug it back in the equation.